基于隐函数的空间非规则体激光点云三维曲面重建及体积计算优化研究
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山东理工大学机械工程学院淄博255049

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TH86TN958

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山东省自然科学基金项目(ZR2023MF046)、淄博市重点研发项目(2021SNCG0053)资助


Implicit function-based 3D surface reconstruction and optimized volume calculation for irregular objects from laser point cloud
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School of Mechanical Engineering, Shandong University of Technology,Zibo 255049, China

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    摘要:

    空间非规则体,如地上建筑物、山坡及地下采空区等,其三维曲面重建与高精度体积计算在现代物流、仓储及矿山测量等领域具有重要应用价值。针对激光点云在真实采集环境中存在的噪声干扰、密度分布不均以及复杂曲面区域法向量估计不准确等问题,提出了一系列优化措施研究,有效提高了三维建模效果和体积计算精度。首先,在传统统计滤波基础上,引入局部密度与曲率特征,提出一种自适应特征保留滤波算法,在有效抑制离群噪声的同时显著降低稀疏区域及高曲率特征点的误删率;其次,针对点云密度分布不均导致法向量估计精度下降的问题,提出一种曲率自适应的法向量混合估计策略,在平坦区域采用主成分分析(PCA)快速估计法向量,在曲率变化显著区域引入二次曲面拟合进行局部修正,从而在保证计算效率的同时提升复杂曲面区域法向量估计的稳定性与准确性;最后,利用平滑符号距离隐式函数实现水密曲面重建,并结合投影-四面体分解法完成体积计算。通过水桶模型、实验室空间及实验室-走廊结合体等多场景实验对所提方法进行验证,所得体积相对误差分别降低至1.63%、0.32%和0.25%。实验结果表明,所提方法在曲面重建连续性与体积计算精度方面均取得了较好效果,可为复杂空间物体的高精度三维曲面重建与体积测量提供一种稳定可靠的技术方案。

    Abstract:

    The three-dimensional surface reconstruction and high-precision volume calculation of spatially irregular objects, such as above-ground buildings, slopes, and underground goafs, hold significant application value in modern logistics, warehousing, and mine surveying. To address the problems of noise interference, non-uniform density distribution, and inaccurate normal vector estimation in complex curved regions of laser point clouds acquired under real-world conditions, a series of optimization strategies are proposed to improve three-dimensional modeling quality and volume calculation accuracy. First, an adaptive feature-preserving filtering algorithm is proposed by introducing local density and curvature features into the conventional statistical filtering framework, which effectively suppresses outlier noise while significantly reducing the misclassification and removal of feature points in sparse regions and high-curvature areas. Second, to overcome the degradation of normal vector estimation accuracy caused by non-uniform point cloud density, a curvature-adaptive hybrid normal estimation strategy is developed. Principal component analysis(PCA) is employed for rapid normal estimation in relatively flat regions, whereas quadratic surface fitting is introduced for local refinement in regions with significant curvature variation, thereby improving the stability and accuracy of normal estimation in complex surface regions while maintaining computational efficiency. Finally, watertight surface reconstruction is achieved using a smooth signed distance implicit function, and volume calculation is performed via a projection-tetrahedral decomposition method. The proposed method is validated through multi-scenario experiments involving a bucket model, a laboratory space, and a laboratory-corridor combined structure. The resulting relative volume errors are reduced to 1.63%, 0.32%, and 0.25%, respectively. Experimental results demonstrate that the proposed method achieves improved surface reconstruction continuity and volume calculation accuracy, providing a stable and reliable technical solution for the high-precision three-dimensional surface reconstruction and volume measurement of complex spatial objects.

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陈波,王建军,王文心,付广洋,尹建程.基于隐函数的空间非规则体激光点云三维曲面重建及体积计算优化研究[J].仪器仪表学报,2026,47(6):137-148

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  • 在线发布日期: 2026-09-02
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